Formaldehyde
In plain terms
A preservative and disinfectant. In personal care it shows up directly in a few products like some nail hardeners, and it is also released by certain hair-smoothing treatments and by some preservatives.
What the evidence shows
Formaldehyde is one of the better-characterized carcinogens still in use. The IARC and the US National Toxicology Program both classify it as a known human carcinogen, tied to nasopharyngeal cancer and leukemia, and it is a skin and respiratory sensitizer as well. The exposure that matters most is breathing it in, which is why salon hair-smoothing treatments that release it when heated have drawn the sharpest scrutiny, for the air both workers and clients breathe. The FDA has proposed barring formaldehyde and the chemicals that release it from hair-smoothing and straightening products, and several US states have already restricted it in cosmetics. Direct use in consumer products is now uncommon, but it persists in some nail hardeners and can hide in goods that release it rather than list it.
On the label
When added directly it is listed as formaldehyde or formalin. More often it is not listed at all, because it is released by another ingredient, such as a formaldehyde-releasing preservative.